Problem: Convert the angle $\theta=\dfrac{23\pi}{20}$ radians to degrees. Express your answer exactly. $\theta=$
Solution: Background An angle can be measured in degrees or in radians. A circle can be divided into $360^\circ$ or $2\pi$ radians. The conversion between degrees and radians is as follows. $\text{Angle in Radians} = \dfrac{\pi}{180^\circ}\cdot\text{Angle in Degrees}$ $\text{Angle in Degrees} = \dfrac{180^\circ}{\pi}\cdot\text{Angle in Radians}$ Converting $\theta$ to degrees Using the formula, we get the following conversion. $\begin{aligned}\text{Angle in Degrees} &= \dfrac{180^\circ}{\pi}\cdot\text{Angle in Radians} \\\\ &= \dfrac{180^\circ}{\pi}\cdot\dfrac{23\pi}{20} \\\\&=207^\circ\end{aligned}$ Summary $\theta=207^\circ$